find the principal unit normal vector to the curve at the specific value of the parameter.

i need to use this formula

so, to find r'(t)

so, now to find the magnitude: simplified

puting them together

From here is where i get lost

I need to find T'(t)

I can seem to follow the solutions manual. I think they are using the quiotient rule due to the denominator having the 3/2

fraction. But if they are i still cant see how they are doing it.

Can anyone help me work out the next step for T'(t)?

Thank you so much!!!